Solving One-Variable Equations with Systems
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Heather is solving an equation by graphing the expressions on either side of the equal signs. If the graph intersects at an
infinite number of points, which statement could describe the equation Heather is attempting to solve?
One side of the equation is a constant, and the other side of the equation is a linear expression.
One side of the equation is a linear expression, and the other side of the equation is a quadratic expression.
One side of the equation is a constant, and the other side of the equation is a quadratic expression.
One side of the equation is a quadratic expression, and the other side of the equation is a quadratic expression.

a

step-by-step explanation:

jjddbdhid r

3/6 chance

step-by-step explanation:

half of the nubers are odd numbers (1,3,5) which in that case if you would be told to simplify it would be 1/2

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt